Azizi, A. and Zekhnini, A. and Taous, M. (2018) On the unit index of some real biquadratic number fields. Turkish Journal of Mathematics, 42 (2). pp. 703-715.

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Abstract

Let p1 ≡ p2 ≡ 1 (mod 4) be different prime numbers such that (2/p2) = (p1/p2) = - (2 p1) = -1. Put K = ℚ(√ 2p1p2) and let K be a quadratic extension of K contained in its absolute genus field K(*) . Denote by kj, 1 ≤ j ≤ 3, the three quadratic subfields of K. Let EK (resp. Ekj) be the unit group of K (resp. kj). The unit index EK: Πj3=1 Ekj is characterized in terms of biquadratic residue symbols between 2, p1 and p2 or by the capitulation of 2, the prime ideal of ℚ(√ 2p1) above 2, in K. These results are used to describe the 2-rank of some CM-fields. © Tübi˙tak.

Item Type: Article
Subjects: Mathematics
Divisions: SCIENTIFIC PRODUCTION > Mathematics
Depositing User: Administrateur Eprints Administrateur Eprints
Last Modified: 31 Jan 2020 15:48
URI: http://eprints.umi.ac.ma/id/eprint/3924

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